Friday, June 9, 2017

Further Examinations on Pyramid and Pentagram

I have had a change of thinking. I would like to reexamine a couple of esoteric symbols thanks to some recent reading.

In my post on the Witch's Pyramid, I wrote the following:
It has come to my attention that, in recent years, the Witches Pyramid has had ascribed to it a fifth principle: "To Go." I believe this is happening from a misguided attempt to correlate the pyramid with the pentagram. The pentagram is a very different symbol and does not discuss the hermetic principle symbolized by the pyramid. The pentagram is a symbol of the unity of the five elements of the universe, not the principles employed by hermetic students to understand how to evolve the spirit. Though I'm fine with people developing whatever mnemonic device they feel is helpful, I do not agree with inventing something that never was while claiming that it did. The pyramid has older names including the "Hermetic Quaternary" and the "Four Powers of the Magus." Both of these names specify four principles, not five, because the new principle that has been invented is clearly not necessary. The four principles are forward-moving principles, so to state that one must then go is redundant to the goal. It also shows a failure to understand what is being taught.
The hermetic magical principles are not symbolized by the corners of the pyramid, but by the faces. There are four triangular faces representing the principles. They are supported by a square face that is hidden. Triangles are symbolic of active properties. Squares are symbolic of manifestation. The surprise to most is that we are not trying to metaphorically travel to the peak of the pyramid. Too many people assume incorrectly that the only way to symbolize the attainment of higher states of being is with a literal movement upward. However, in this case, what is revealed comes from looking at the face of the pyramid that we cannot see. On each of the active faces rests one of the elemental angels, as we saw in the Wheel of Fortune, above. On the base is the manifested figure of the Sphinx herself, for she represents the unity of the elements. Only through unifying the powers of the elements do we gain manifestation. This is the core lesson of magical work.
My change of thinking is not about the reinvention of the Witch's Pyramid to have 5 principles. I still believe contemporary magicians should not try to muck with an axiom that works. Rather, I am seeing more connection between the pyramid and the pentagram. This change of thinking is not simplistically caused by the fact that both feature the number 5; there are deeper connections at work. I would like to explore them and expose more of my thinking on the matter.

I also wrote in the previous entry a little about the riddle posed by the sphinx to Oedipus. Let's look at that riddle so we have it before us (Apollodorus, 3.5.8).
And having learned a riddle from the Muses, she sat on Mount Phicium, and propounded it to the Thebans. And the riddle was this: What is that which has one voice and yet becomes four-footed and two-footed and three-footed? . . . Oedipus found the solution, declaring that the riddle of the Sphinx referred to man; for as a babe he is four-footed, going on four limbs, as an adult he is two-footed, and as an old man he gets besides a third support in a staff.
Note that I stated that squares are symbolic of manifestation. That is an important link to understand the potential divinity in man. Our bodies are material things, made up of the four elements unified on this material level. But on a divine level, there is a reflection of our bodies ("as above, so below"). That reflection is also made up of the unified elements, but in the divine sense; the elements are not material, they are spiritual. They are the elements about which Levi spoke. They are the non-material principles that together make up the spirit. That which is opposite to the peak of the pyramid is the base of the pyramid. So if the peak is our spirit self, which is conveniently represented as a point with no dimension, the base is our body, which is also conveniently represented by the square, the symbol of the material in balance. I have already mentioned in the last entry that the base is also represented by the sphinx herself, a being still in this material plane, but incorporating all of the elements. She is the Magus.

What changed the connection between the pyramid and the pentagram was a passage from an occult writer I greatly respect, though more current than Levi. Here is a passage (translated) from The Practice of Magical Evocation by Franz Bardon:
When practicing evocation or invocations of beings, it is desirable to draw within the center of the circle in which one is to stand another smaller circle or a pentagram with one of its points upwards, the symbol representing man. This is then the symbolization of the small world, of man as genuine magician.
So here we read that Bardon reveals the symbolism of the pentagram be symbolic of man. Allow me to provide an image that may help illustrate this point. It is by Agrippa, from book two of his Three Books of Occult Philosophy, 1651.

Next, let's recall the associations between the pentagram and the elements, which has come down to us through tradition from the mystery schools.

So we can see that the pentagram embodies both the elements and the body of man. But does this analogy only seem solid because both coincidentally incorporate the number five? Does the connection between the pyramid and the pentagram go deeper? Considering the image above, what happens if we lose one element? Five becomes four. Suppose that the element above called "spirit" is more correctly "divinity." Without the divine, one is a creature with four elements only, much like the sphinx - the base of the pyramid.

For one to travel from the base of a pyramid to its peak - to metaphorically evolve from the material plane to a divine one that is without dimension - one must travel up each (perhaps all) of the four triangular faces. To do this on a material pyramid, one would travel a distance that the Greek mathematicians called "phi"

The value of phi was so important to the Greeks that it was used as the basis of all of their architecture and was called the Golden Mean and the Divine Portion. Interestingly, the same value is found all over the pentagram.

The shape of man's body is also packed with phi, which is illustrated by this image very well (represented by any section labeled M, where E is the value of 1).

So it is true that the Hermetic principles are symbolized by the faces of the pyramid, rather than by the corners. But it is also true that there is a divine relationship between the symbolism present in both the pyramid and the pentagram. Both are helpful to understanding the lessons found in the witch's pyramid as a guide to evolving the spirit. Both point to the power inherent in man.

Thursday, June 8, 2017

More Math in Magic Squares

This entry is a continuation of my last blog entry on planetary sigils and kamea. It is the entry with all the math and odd speculation that makes a blog entry boring. So if reading about investigation and the process of decoding puzzles isn’t your thing, feel free to skip over this one. But if you are the least bit curious about the Solomonic sigils, you might want to take a peek.

First, let’s remember that there are sigils for both the planetary intelligences and the planetary spirits. We saw in the last blog entry how those two groups of sigils are created using numerology and names.

But there are also sigils simply called “planetary seals.” Here are images from around the web of how each of the planetary sigils are traditionally drawn. I will note that the seal of Saturn is my own drawing because the web is currently circulating all sorts of non-traditional garbage for what is probably the easiest drawn seal in all of ceremonial magic. (Witches, please check your work!)

Sigil of the Moon (9)

Sigil of Mercury (8)

Sigil of Venus (7)

Sigil of the Sun (6)

Sigil of Mars (5)

Sigil of Jupiter (4)

Sigil of Saturn (3)

These sigils are not drawn using the same method we examined previously, but I did get curious how they were created. I also began to notice some odd characteristics of the seals and the kameas.

I first noticed that the sigil of Saturn is drawn over that planet’s kamea using a very obvious technique. The numerals are divided into three sets of three. The numerals of each of the sets are connected with lines, separate from each other. A circle starts and ends each connecting line. I’ll illustrate that here by removing the numbers and using colors so it’s easy to highlight some of the characteristics of this seal. We will observe those characteristics later.

Saturn Drawing

Notice how the seal has bilateral symmetry with the axes of symmetry falling on the whole kamea's diagonals. The middle set of numerals also creates a line of symmetry (in red). The sets before and after the middle set make designs that are reflections of each other. Also, there is a convergence of lines on both sides of the center block.

I don’t know why this one planetary sigil was drawn using this technique, while the others were not. But I began to wonder what would happen if I applied these drawing methods to the other kameas. Allow me to walk you through my process.

So let’s draw on the other kameas, but only those that are based on odd numbers for now. Using the same methods we observed in the sigil of Saturn, we first write down all the numerals of each square and divide them into sets appropriate for the planetary number, then we draw out each numeral set using circles to start and end each set. Some interesting designs appear. We can see that there is bilateral symmetry in them. Again, the numeral set in the middle creates one of the lines of symmetry (in red). Each of the pairs of numeral sets on both sides of the middle set create designs that are reflections of each other. Also, all the beginnings and endings of the numeral sets straddle the diagonal (with the exception of the middle set). I’ve illustrated all of this with colors again to make it all easier to see.

Mars Drawing

Venus Drawing

Moon Drawing

What this shows is that the odd numbered kameas represent the symmetry inherent in mathematics. In order for all the rows and columns of blocks to sum the same, the very largest number must be placed opposite to the very smallest, then the next largest and smallest, and so on until the middle of the available numbers is reached. This isn’t magic, it’s just math. We can also see from the patterns that all of the odd numbered kameas are based on a similar numeral arrangement, but just increase their complexity as the kameas get larger. This makes the convergence that we saw on both sides of the middle block no longer the only convergence.

Let’s apply the same drawing methods to the even numbered kameas and see what happens. Jupiter and Mercury also show a bilateral symmetry. Since there is no middle numeral set, the sets simply pair up evenly without it. However, now the axes of symmetry have been rotated 45 degrees from the diagonals to the vertical and horizontal. Also, the start and end of each set has moved to the outer blocks. A convergence of lines becomes prevalent, only now all of the numeral sets is contributing. Here are more colors to illustrate all of this, though Mercury started to get visually busy, so I separated the first four numeral sets from their mates. This also helps to show the symmetry that is happening, as the first four sets create a mirror image of the last four sets. Notice also that a pentagram is starting to appear in Mercury's crossing lines.

Jupiter Drawing

Mercury Drawing

The odd man out in all of this is the kamea of the Sun. When we start to draw the lines from the sets, we quickly notice that there is no symmetry! Drawing it to the end shows that there is only one point of convergence to the right of center and there are several sets that force a drawn line to be back-tracked, which never happens in any of the other kameas. However, the sets do begin and end only on the outer blocks. I've separated the mates of the pairs, as I did in the Mercury drawing, to show the lack of symmetry.

Sun Drawing

Since I know that there are many different arrangements of numbers that can create a magic square still fulfilling the row and column summation rule, my first thought was that tradition had brought down to us the wrong 36-block kamea for this planet – one without symmetry. So, I tried to build a kamea that fit the rules displayed by all the other kamea. This proved impossible. Here’s why it’s impossible.

For an even numbered kamea to have bilateral symmetry, the base number must be divisible by 4, because bilateral symmetry creates a reflection (two images) on two planes, which creates quadrants of images (2 images x 2 planes = 4 images). Imagine a kaleidoscope that only produced four images inside it. Odd numbered kameas don’t have this problem because one of their numeral sets creates one of the needed lines of symmetry; a midline will always be built into those drawings. If we had kameas with a base of 10, 14, 18, 22, 26, etc., they would all show the same problem with bilateral symmetry, because they are all even numbers that are not divisible by 4. Again, this isn’t magic, it’s just math, though I will agree that math, particularly as it applies to shapes (geometry) can be very sacred.

By now you have likely wondered exactly what technique was used to create all those sigils of the planets that have come down to us - the ones at the very beginning of this entry. Well, unfortunately, no one knows. The best hypothesis I’ve seen to date was done by a clever Rosicrucian, who speculated that a counting technique was applied to the kameas. That information can be found here. For now, we simply accept that it is knowledge lost to the past.

If any of you have done work with kameas and planetary sigils, please comment your insights below or link the rest of us to your pages.

Thanks for indulging my mathematical deviation.

Tuesday, June 6, 2017

Magic Words and Sigil Magick

Recently, I was working with sigils (again). I was reviewing the methods used by modern Hoodoo practitioners to make Key of Solomon-style sigils. It’s fascinating stuff, but there are some elements that are shortcut. I’ll explore sigils here in an attempt to provide connections between several very deep topics.

I apologize in advance if something I write seems as if I’m being cursory. One could likely write a long book about all this. However, as this is only a blog, my goal is to show you the connections, so that you will better experience the wonder that I felt when all this began to become meaningful for me.

Mankind began with sounds, which he modulated in the mouth. That led to an attempt to make symbols to represent the sounds – as stated in the movie, The Dark Crystal, “words that stay.” Writing was born. Let’s explore speech and writing separately.

Since much of what comes down to us in the Western Mystery schools comes from the Kabbalah, we should start in the Ancient Near East. Kabbalah was highly influenced by Babylonian numerology and astrology, which was also influenced by ancient Hindu principles through trade routes. Kabbalah then lent its systems to Greece.  A bit later, I’ll show a tiny bit how each of these cultures contributed.

Speaking is represented in myth as a very special and creative event. Yahweh created the universe by speaking it into being. The Memphite (Northern Egypt) creator, Ptah, created things by what was described as an act of the heart and the tongue. It’s important to note that the people of the ANE didn’t view ideas as living in the brain. Mummification (and warfare) gave people an understanding that there was an organ in the skull, but no one knew what it did. Thinking was done in the chest – in the heart – where ideas lived. So an action of the heart and the tongue was an action of generating an idea and then making it known to the world. This was such a powerful concept that it led to the esoteric idea that knowing the name of a thing could give you power over it.  Certainly, it gave you the power of creating it, because until it was named, its creation process was not complete and so it was not a real thing. For this reason, Yahweh brought all of the animals to Adam to be named. Each of them needed an identity.

The Hindus have mantras. Mantras are phrases spoken over and over, perhaps thousands of times, to bring a desired change to your life by manifesting what is needed. Mantras are made up of “seed sounds.” These are the basic and core sounds used to form more complex words. Yet these sounds are not simply utterances. They are mystical vibrations that modulate the resonance of the universe to bring things into being. By speaking these seed sounds in the correct order, vibrations move out into the universe to bring about the desired changes. Often, these changes occur in the mind of the speaker.

But why does the power to create something give you power over it? To the mythic mind, creation and destruction are the same process. Raw materials are destroyed and remade as something else. What was mud or an elder tree became man. What was the body of a titan, became the land, sea and sky. To gain the power over a thing, you simply need to know what it is called. This is the reason secret societies (like witches in covens) have inner-circle names that are never shared. This is also the reason why divine names become magic words of power. (A completely acceptable charm is to write the name of a deity on paper, then fold it into a bundle to be tucked into a mojo bag or a fold in your clothing, to summon the powers of that deity.) Any word can be used as a magic word because it identifies an essence.

Many cultures believed, and so represented, the invention of writing as a sacred event, often telling tales of writing systems as gifts from their gods. Odin brought the runes to mankind; Thoth brought hieroglyphics. Because writing was a lasting representation of a sound, which was the word of power naming a thing, the glyph itself had the power of the sound. It was a representation of the very essence of the created thing.

Just as alchemy was the forerunner of chemistry, so numerology was the forerunner of mathematics. The Babylonians loved their numbers so much that they would actually use numbers to refer to their deities as a kind of short-hand honorific. For example, if the number that represented you was the number 123, I could simply refer to you in conversation like this, “123 and I had a great time in circle,” which would be a gesture of respect, because your number is your essence. Transmitted from the Babylonians throughout the ANE was the idea that the glyphs of sounds correspond to numbers.

Pythagoras was a clever Greek when he discovered music theory. Vibrations could be created by mathematically dividing a vibrating string. Interestingly, the vocal cords are simply vibrating strings that are similarly modulated like the stretched stings of a lyre. This shows a deep connection between mathematics and vibration; as such, every sound corresponded to a particular numerical value. If every sound has a glyph, and every sound also has a numerical value it means that every glyph has a value.

Because speaking, singing, writing, language and mathematics are not enough, let’s bring astronomy into this. The Magi of Babylon were expert astronomers as well as accomplished mathematicians. In the Babylonian sky were seven dominant heavenly bodies. Their gods ruled over sections of the sky and were embodied by the seven observable heavenly bodies, which were mathematically chartable. To state that they believed numerals to be divine was an understatement! The Babylonian custom used mathematical sums as a substitution for the names of their gods as a kind of respectful short hand. So numbers represented their gods, but also the planets.

They assigned a number to each of the planets based on its speed through the heavens. Saturn, the slowest planet observed, received the smallest number, 3, followed by Jupiter, Mars, The Sun, Venus, Mercury, and finally The Moon, which was the fastest body gaining the number 9. (Incidentally, this is also how the planetary hours are ordered in ceremonial magic charts. I have also seen some schools of thought that use this planetary rulership for the seven chakras.)

Each of the assigned numbers were used to create magic squares, or “kamea.” Kamea are traditional Babylonian and Kabbalistic grids that contain both rows and columns equal to the planetary number. In each block of the grid is placed every numeral from 1 through the square of the planetary number. For example, in the kamea of Saturn, there are 3 rows of 3 columns containing the digits 1 through 9 (32). The numerals are placed so that every row and column, as well as the major diagonals, have the same sum. In the case of Saturn, each row and column has the sum of 15. However, there are many different ways to arrange the numerals in the kamea to still accomplish the uniform sum. So there are traditional arrangements of the digits that have been passed down. Below are the traditional kamea of all the planets.

The idea that names held power permeated the Kabbalah, which was used to compose some of the most famous source books for magical systems in the world, The Keys of Solomon. Anyone who has ever opened a cover of these books knows they are filled with Solomon’s “seals.” These seals are simply arrangements of sigils creating designs that can be inscribed on metals to create charms. Often, the charms are purported to allow the holder to gain power over certain spirits or intelligences. The designs accomplish this because they contain the names of these spirits and intelligences represented as glyphs. The method for creating these glyphs uses sound and numerology to create a written symbol of power.

In Kabbalah, each of the planetary intelligences and spirits have a name made up of a string of sounds, just like your own name. Their name is their word of power. Each spirit is associated with a ruling planet, which has a kamea. If we convert the sounds in the name into numbers, then connect the numbers using the correct kamea, we create a glyph for each name that magically represents each spirit.

Observing just a few standards, you can use the same method to make your own sigils of your name, or of any other word that is powerful to you. Contemporary Hoodoo uses an adaptation of this method. It is an easy method, but it does deviate from the Kabbalist method just a bit. I’ll describe the Kabbalist method used above a bit later.

For the hoodoo method, use the following table to convert all the letters in your name to numbers.

Now choose the kamea that rules over your natal zodiac.

Now simply draw lines to connect the numerals in the kamea in the order of the name. Here are the drawing standards that seem apparent to me based on the sigils in the Keys of Solomon. First, no line should ever be back-traced, which means that every time you visit a block, you should use a unique line. It also means that when returning to a block that already has a line stop, you should stop at some other place in that block. Second, double numbers should have a small wave or bump to show that the block was marked twice (or more). Finally, the first numeral should be marked with a small circle.

Here is an example of the sigil for Hagiel, the intelligence of Venus, which shows a repeated letter and parallel lines, but no lines are completely back-traced. Notice that returning to block 3 required that we put a stop in a different part of the block, rather than intersecting with the one that was already there.

Despite the rules, you can flex your creativity a bit. It appears acceptable for the stops in each block to be rounded rather than sharp points, or to go from block to block using arcs, rather than straight lines, so long as the arcs are consistent. The last numeral can be marked in many ways, such as with a final circle, a small perpendicular line, a wave, a chevron, or simply stopping. The sigil is your creation and it carries the power you put into it.

You can also build sigils for other words that are powerful to you, such as “health” or “money.” You would simply use the kamea appropriate for those purposes. These are the accepted hoodoo associations of each of the planets.
Sun: Health, vitality, ego, power, success, advancement, leadership, and growth
Moon: Clairvoyance, sleep, emotions, astral travel, imagination, women, birth, and reincarnation
Mars: Male sexuality, strength, lust, anger, destruction, medical issues 
Mercury: Communication, intellect, writing, contracts, information, wisdom, science, memory
Jupiter: Success, abundance, money, growth, gambling
Venus:  Love, pleasure, female sexuality, arts, music, beauty, luxury, social affairs
Saturn:  Real estate, banks, debt, obstacles, binding, knowledge, time, discipline

If you are feeling a bit nefarious, you can also build a sigil to represent another person to gain power over them.

The difference between the hoodoo version and the Kabbalistic version is that the latter relies on sound, rather than just letters. Rather than the names being converted based on the letters used to write the name, they are converted based on the sounds that are used to construct their utterance. The values of each sound can be found in the following table (Mathers, 3). Note that the values for the sounds k, m and n differ when they are final sounds than when they are elsewhere in the word. For the sound made by w, use v. There is no letter e. Short vowels are generally ignored, which leaves the sound created by an e represented by either the long a or the long i, depending on which sounds closer.

Also note that there are values that are too large for some kamea. In that case, simply drop zeroes until the number fits. For example, the name “Tom” would be a strong T (9), then O (70 or 7), then a final M (600 or 60 or 6, not 40). The name “Steve” would be S (60 or 6), a strong T (9), a long ee sound, represented by the I, Y (10 or 1), then a V (6). The final vowel is silent.

Oddly, the numerology table used in hoodoo is the one also used in so-called “Pythagorean numerology.” This is an odd name to me because the Greeks had an alphabet of sounds, just as in Kabbalah and were big fans of assigning numbers to the sounds made by their alphabet. This was a very popular process called Isopsephy and was used even for very mundane affairs. They did not have letters that made multiple sounds as we do in English. It seems to me that the best Pythagorean numerology table would be based on sounds and would use the original isopsephographic values that the Greeks used so often. That translated table would look like this.

The value for each row in the table increases by a factor of 10. So G is worth 3 and L is worth 30, while T is worth 300.

Whether you use the Hebrew, the Isopsephy or the “numerology” table to assign values, you now have all you need to move forward in sigil magic.

For more information on the numerology of the Babylonians, investigate Trail of the Serpent by Christian writer, Murl Vance.


Mathers, S. L. Mac Gregor. The Kabbalah Unveiled. Theosophical Publishing Co., New York. 1912.

If you have any interest in diving into a more mathematical look at the kameas, feel free to look at my next entry, found here.